1. Gain = (S.P.) - (C.P.)

2. Loss = (C.P.) - (S.P.)

3. Loss or gain is always reckoned on C.P.

4. Gain Percentage: (Gain %)

Gain % = (Gain x 100)/C.P.

5. Loss Percentage: (Loss %)

Loss % = (Loss x 100)/C.P.

6. Selling Price: (S.P.)

SP = {[(100+Gain%)/100]*C.P.}

SP = {[(100-Loss%)/100]*C.P.}

7. Cost Price: (C.P.)

CP = {[100/(100+Gain%)]*S.P.}

CP = {[100/(100-Loss%)]*S.P.}

8. If an article is sold at a gain of say 35%, then S.P. = 135% of C.P.

9. If an article is sold at a loss of say, 35% then S.P. = 65% of C.P.

10.When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:

Loss % = (Common Loss and Gain %/10)^2 = (x/10)^2.

11.If a trader professes to sell his goods at cost price, but uses false weights, then

Gain % = {[Error/(True Value-Error)]*100}%

### General Tips

Cost Price:

The price, at which an article is purchased, is called its cost price, abbreviated as C.P.

Selling Price:

The price, at which an article is sold, is called its selling prices, abbreviated as S.P.

Profit or Gain:

If S.P. is greater than C.P., the seller is said to have a profit or gain.

Loss:

If S.P. is less than C.P., the seller is said to have incurred a loss.

Example 1

A trader buys 8 oranges for Rs 1o and sells 9 Oranges for Rs 11. What is gain or loss in percentage?

Solution :

Steps 1 : Buy 8 Oranges for RS 10

Step 2: Sells 9 Oranges for Rs 11

Step 3 : (8 x 11)– (10x 9)/(10 x 11) [ Mark the cross relationship]

Step 4: 88-90/110 = (-) 2/110

Answer is Loss of 0.018 %

Example 2

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

Solution:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

Gain =[(80/1600)*100]% = 5%.